4. The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.


(i) In which subject did the student score 105 marks?

(ii) How many more marks were obtained by the student in Mathematics than in Hindi?

(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

(i) For 540 marks, the central angle = \( 360^{ \circ}\)
∴ the central angle for 1 mark = \(\left( \frac { 360 }{ 540 } \right) ^{ \circ }=\left( \frac { 2 }{ 3 } \right) ^{ \circ }\)
∴ the central angle for 105 marks =\( \left( \frac { 2 }{ 3 } \times 105 \right) ^{ \circ }=70^{ \circ }\)

Hence, from the given pie chart, the subject is Hindi.
(ii) Difference between the central angles made by the subject of Mathematics and Hindi= \(90^{\circ} – 70^{\circ} = 20^{\circ}\).
Marks obtained for the central angle of \(360^{\circ}\), = 540 Marks obtained for the central angle of \(1^{\circ}\)=\(\frac { 540 }{ 360 } =\frac { 3 }{ 2 }\)

Marks obtained for the central angle of \(20^{\circ}=\frac { 3 }{ 2 } \times 20=30\)

Hence, the student obtained 30 more marks in Mathematics than Hindi.

(iii) Sum of the central angles made by Social Science and Mathematics =\( 65^{\circ}+ 90^{\circ} = 155^{\circ}\).
And, the sum of the central angles made by Science and Hindi = \(80^{\circ}+ 70^{\circ} = 150^{\circ}\).

Since \(155^{\circ} >150^{\circ}\), therefore, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.